Neighborhoods for entailment

Journal of Philosophical Logic 32 (5):483-529 (2003)
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Abstract

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the Routley-Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable

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Citations of this work

Tracking reasons with extensions of relevant logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.
Neighbourhood Semantics for Quantified Relevant Logics.Andrew Tedder & Nicholas Ferenz - 2022 - Journal of Philosophical Logic 51 (3):457-484.
Information Flow In Logics in the Vicinity of BB.Andrew Tedder - 2021 - Australasian Journal of Logic 18 (1):1-24.
Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.

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References found in this work

Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
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Advice on modal logic.D. Scott - 1980 - In Karel Lambert (ed.), Philosophical problems in logic: some recent developments. Hingham, MA: Sold and distributed in the U.S.A. and Canada by Kluwer Boston. pp. 143--173.
Pragmatics and intensional logic.Richard Montague - 1970 - Synthese 22 (1-2):68--94.

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